We present single dish and interferometric maps of several rotational transitions of HC _ { 3 } N vibrationally excited levels towards Sgr B2 . HC _ { 3 } N is a very suitable molecule to probe hot and dense regions ( hot cores ) affected by high extinction since its vibrational levels are mainly excited by mid-IR radiation . The single dish maps show , for the first time , that the HC _ { 3 } N vibrationally excited emission ( HC _ { 3 } N* ) is not restricted to Sgr B2M and N but extended over an area 40 ^ { \prime \prime } \times 20 ^ { \prime \prime } in extent . We distinguish four bright clumps ( Sgr B2R1 to B2R4 ) in the ridge connecting the main cores Sgr B2M and Sgr B2N , and a low brightness extended region to the west of the ridge ( Sgr B2W ) . The physical properties and the kinematics of all hot cores have been derived from the HC _ { 3 } N* lines . Our high angular resolution images show that the Sgr B2N hot core breaks in two different hot cores , Sgr B2N1 and N2 , with different radial velocities and separated by \sim 2 " in declination . We find that the excitation of the HC _ { 3 } N* emission in all hot cores can be represented by a single temperature and that the linewidth of the HC _ { 3 } N* rotational lines arising from different vibrational levels systematically decreases as the energy of the vibrational level increases . The systematic trend in the linewidth is likely related to the increase of the velocity as the distance to the exciting source increases . We have developed a simple model to study the excitation of the HC _ { 3 } N vibrational levels by IR radiation . We find that the single excitation temperature can be explained by high luminosities of embedded stars ( \sim 10 ^ { 7 } L _ { \odot } ) and small source sizes ( \sim 2 - 3 ^ { \prime \prime } ) . The estimated clump masses are 500 M _ { \odot } for Sgr B2M , 800 M _ { \odot } for Sgr B2N and 10-30 M _ { \odot } for Sgr B2R1 to B2R4 . Luminosities are 1 - 2 10 ^ { 6 } L _ { \odot } for Sgr B2R1-B2R4 and Sgr B2M and 10 ^ { 7 } L _ { \odot } for Sgr B2N . We estimate HC _ { 3 } N abundances of 5 10 ^ { -9 } for Sgr B2M and Sgr B2N2 and 10 ^ { -7 } for the rest of the hot cores . The different HC _ { 3 } N abundances in the hot cores reflect different stages of evolution due to time dependent chemistry and/or photo-dissociation by UV radiation from nearby HII regions . According to the mass and the luminosity of the different hot cores , we propose that Sgr B2M and B2N contain a cluster of 20-30 hot cores , each like that in Orion A , a number similar to the UC HII regions already detected in the region . The Sgr B2R1-B2R4 hot cores represent isolated formation of massive stars .